code: def test_PrimeIdeal_eq():
      # `==` should fail on objects of different types, so even a completely
      # inert PrimeIdeal should test unequal to the rational prime it divides.
      T = Poly(cyclotomic_poly(7))
      P0 = prime_decomp(5, T)[0]
      assert P0.f == 6
      assert P0.as_submodule() == 5 * P0.ZK
      assert P0 != 5
  
imports: from math import prod
  from sympy import QQ, ZZ
  from sympy.abc import x, theta
  from sympy.ntheory import factorint
  from sympy.ntheory.residue_ntheory import n_order
  from sympy.polys import Poly, cyclotomic_poly
  from sympy.polys.matrices import DomainMatrix
  from sympy.polys.numberfields.basis import round_two
  from sympy.polys.numberfields.exceptions import StructureError
  from sympy.polys.numberfields.modules import PowerBasis, to_col
  from sympy.polys.numberfields.primes import prime_decomp, _two_elt_rep, _check_formal_conditions_for_maximal_order
  from sympy.testing.pytest import raises
label_desc: Use image node_id 12 for calling a global function with example usage: test_PrimeIdeal_eq() without return types